Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 3

BPS spectrum, wall crossing and quantum dilogarithm identity

Pages: 405 – 524



Dan Xie (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)


BPS spectrum with finite number of states are found for higher rank four dimensional $N = 2$ theory engineered from six dimensional $A_{N-1} (2, 0)$ theory on a Riemann surface with various kinds of defects. The wall crossing formula is interpreted as the quantum dilogarithm identity. Various methods including quiver representation theory, maximal green mutation, and cluster algebra are used extensively. The spectral generator and its refined version for the higher rank theory are written down using the explicit spectrum information. The finite chamber has an interesting $N^3$ behavior in the large $N$ limit.

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Published 19 October 2016